PURPOSE: Understanding the relationship between an environmental determinant and a given health outcome is key to inform public health policies. The short-term mortality and morbidity responses to outdoor air pollutants are traditionally assessed as a log-linear relationship, but few studies suggest a possible deviation from linearity. This paper investigates the shape of the relationship between ozone, NO(2) and fine particulate matter (PM(10) and PM(2.5)), mortality and hospital admissions in 18 French cities between 2000 and 2017. METHOD: A multi-centric time series design, using quasi-Poisson generalized additive models, was used. Four approaches were compared to model concentration-response curves (log-linear, piecewise-linear with a priori defined breakpoints, piecewise-linear with no a priori breakpoint and cubic spline). RESULTS: All the models indicated evidence of supra-linearity between PM(10), PM(2.5), NO(2), mortality and hospital admissions. For instance, with a log-linear model, a 10 µg/m(3) increase in PM(2.5) was associated with a 0.4% [95% CI 0.2; 0.7] increase in non-accidental mortality. When using a piecewise model with a priori set breakpoint at 10 µg/m(3), the mortality increase was 3.8% [4.4; 6.3] below 10 µg/m(3), and 0.3% [0; 0.6] above. Non-significant impacts of ozone were found for concentrations below 90 µg/m(3) to 120 µg/m(3), with some variability in the identified threshold across the heath indicator studied. CONCLUSION: The supra-linearity of the relationship between PM(10), PM(2.5), NO(2), mortality and hospital admissions supports the need to further reduce air pollution concentrations well below regulatory values.